For calibration of the bending stiffness of microforce sensors and/or microforce standards, a microforce measuring device, based on a compensation balance (Sartorius SC2: measuring range 20 mN, 1 nN resolution, 2.5 nN reproducibility, 9 nN linearity deviation, 0.1µN uncertainty) nd a precision linear adjusting device (PIFOC: 80 µm traverse path, 1 nm resolution) has been developed.

Prinzipskizze der Nanokraftmesseinrichtung auf Basis einer Kompensationswaage

Figure 1: Principle of the force measuring device based on a compensation balance

If the standard to be calibrated has a probing tip of its own, this tip is used for probing of the load receptor. At the same time, the deflection z of the standard and the force F required for it are measured. In the case of the compensation balance used, the position of the load receptor remains constant during calibration, i. e. the displacement of the standard z corresponds to the deflection of the standard to be calibrated. The bending stiffness k is calculated as a quotient of the force F and the deflection z.

Figure 2: Microforce measuring device

An essential disadvantage of this force measuring device is its traceability to the SI units with the aid of mass standards. The achievable uncertainties of mass standards are insufficient, especially for small masses. A typical measurement uncertainty for a mass of 1 mg is 20 µg. The gravitational force which corresponds to this mass is thus affected by an uncertainty of 200 nN.

Test of a new electrostatic nanoforce measuring principle

For the assessment of a new electrostatic nanoforce measuring principle based on a disc pendulum between two external electrodes and interferometric deflection detection, a test arrangement has been established and first measurements were performed. Essential characteristics of this principle are electrostatic stiffness reduction and the electrostatic deflection compensation of the disc pendulum. The stiffness reduction of the pendelulum is indispendable for the achievement of a small measurement uncertainty.

Grafik: Testeinrichtung zur Prüfung eines neuen elektrostatischen Nanokraftmessprinzips

Figure 3: Test arrangement for the checking of a new electrostatic nanoforce measuring principle
1: base plate, 2: aluminium disc pendulum, 3 und 4: external aluminium electrodes, 5: thin copper wire, 6: frame connected to base plate, 7, 8: electric insulation layer, 9: permanent magnets, 10: bronze plate, 9 und 10: eddy current brake, 11: laser beam, 12: lens,
acting force: < 10^-10 N (5 mW laser power, HeNe-Laser λ = 633 nm), pendulum length ℓ = 0.2 m, distances between the capacitor faces d₁ = d₂ = 10^-4 m

Figure 3 shows a sketch of the measuring arrangement. The disc (2) having a mass of 2 g is suspended on two copper wires and is situated between two ring electrodes (3, 4).
In first experiments, a stiffness reduction from 0.1 N/m to 0.003 N/m was achieved by applying an electrical voltage between the ring electrodes and the disc.
The principal disturbance variable of the new nanoforce measuring device is seismic noise. To reduce this influence, two identical disc pendulums were used: a measuring pendulum and a reference pendulum. The reference pendulum serves to measure and eliminate the seismic variations and the thermal drift. The complete set-up stands on a pneumatically damped optical table with active inclination stabilization. A large pendulum (m = 200 kg), which can be deflected with the aid of a nano-positioning device, acts as adjusting element of the control device. Without inclination stabilization, the variation of the table in pendulum direction amounts to 1× 10^-6 rad/h, with inclination stabilization, this value is reduced to 1× 10^-8 rad/h. This value is sufficient for the measurement of nanoforces.
A first force measurement for determination of the resolution has been performed with a stiffness reduction to 0.003 N/m. With a measuring duration of 100 s, force resolution was < 0.1 nN. By this, a first proof of the efficiency of this measuring principle has been furnished. An improved establishment in vacuum is under preparation and will soon be available for first nanoforce measurements.